Clarification regarding "Image Crowd Counting Using Convolutional Neural Network and Markov Random Field"
I will try to do it part by part :


  We employ the residual network, which is trained on ImageNet dataset for image classication task, to extract the deep features to represent the density of the crowd.


If you look at the figure 2, you can see that they use the Neural network architecture ResNet. This is a deep network, here is the paper. It has good performance and do image classification.


  This pre-trained CNN network created a residual item for every three convolution layer to bring the layer of the network to 152


If you are in the layer k, it means this layer has in input, the ouput of the k-3th layer. See the paper, figure 5 explains it well without much explications needed. Furthermore, Resnet has 3 different architectures wih different number of layers, and they take the deeper one, the 152 layers deep Resnet.


  We resize the image patches to the size of 224 × 224 as the input of the model and extract the output of the fc1000 layer to get the 1000 dimensional features


The input of Resnet is images of size 224x224, so they need to resize them to fit the input requirement of Resnet. The output of Resnet is 1000 because Imagenet is a dataset of 1000 classes.


  The features are then used to train 5 layers fully connected neural network. The network's input is 1000dimensional, and the number of neurons in the network is given by 100-100-50-50-1.


Then they give the output of Resnet to their own Network, which is 5 layer deep. See figure 2 of their paper. Obviously, the input layer has 1000 inputs because of the output of Resnet. The network have layers of 100, 100, 50 and finally 1 neuron. See figure 2.


  The network's output is the local crowd count


I don't think I need to explain it, they want only the number of people in the crowd, so they need only one output. This is obviously not a classifcation problem, but a regression problem.

Has you don't really point out what you don't understand, I don't explain it in details. Feel free to ask more precise question if some part are still blurred to you !